1 + 1/3 + 1/9 + 1/27 +...

1 + 3+ 9 + 27 + ...

Sn

Sn

Sec 12.4 - Infinite Geometric Series •Finite vs. Infinite Geometric Series What is a finite geometric series?

SUM o f <\ l » i f Of * *

Example:

What is an infinite

Example:

2 f fU geometric series?

2 f \(p +

<iV>+TR(K-edl

\IVA-

ITftt-

ty X/^

10-Lf

lo'tf -f--

-tw-fo

/ /

• *

as «K -e\\()^

hot flo ^ " L ^

Partial Sums What is a partial sum?

For the given series, find and graph the partial sums S» for n - 1 ,2,3,4 and 5. Describe what happens to S„ as n increases. ex 1 3 3 3 3 3

- + - + - + — H- — + 2 , 8 . 32 . 128

512

JUCAJ 3

s4=IEaSi&HI s5 = q&o t/66?5 cpwa ' ^ u ^

ex 2

&=trj

S4=TJSD s3= £ ^ H

1 + I + 2 + E + H + 4 4 4 4 4

r^wl

r-3

^ I W j e ^

*I8

2̂ * &>

P3

± S z S, -? co

V\

•Convergent vs. Divergent Infinite Geometric Series What is a convergent infinite geometric series?

Example:

0>5 + • ( 9 . 1 5 - f ( 9 - 1 ^ 5 + - -

r = i = o.e What is a divergent infinite geometric series?

I ^ f 3 f ' Example:

(5,5 i - U 14- U r'-^^-u

Sum of an Infinite Geometric Series What is the sum of a finite geometric series?

What is the sum of an infinite geometric series?

NO £ U |\\ . H »« ^ ^

5 - — Find the sum of the infinite geometric series, if it exists. ex 1

n - l H

—~>AC\ _ "M

s 9(rf - s(0

<iO \ ~r

--Eel

ex 2 n - l .o-i

^nr-» 'Ob

?*/3 <?—- 4 |

I-2& Soo =̂̂ li M

ex 3 ex 4 i - l Zi(l) •2. t g

Ho Suw

ex 5 ex 6

S _ 4l _ -5 oo 1 - ^ | - - ? / u

ex 7 1 1 1 1 2

>\8 ~12 + 18~27 + 81 -*/r2

ex 8

\

Oofv "" <\, - Vz>

' O b v-v

1

3 o Tog

" 7 /

/̂o S a ^

m=l 't

l"=|.05 W

MO 5^H J

2 3 9 27

% > l i

(\|o SUVK,